I had the exact same symptoms as the original question-asker and I can attest to ISOPROPYL ALCOHOL being all that I needed to fix the issue. I had no cracks and the bit of plastic that presses onto the button was fully intact.
I did opt to open up the controller and remove the plastic pieces, exposing the little buttons for LB & RB. Using a small screwdriver, I depressed both small buttons and with my problem button I had to press a lot firmer with the screwdriver to register a click (I put the batteries back in and was in a game so I could test click sensitivity).
At any rate, I used a spray bottle with the alcohol to spray down into the button and then just started clicking that little button with the screwdriver so that the alcohol would work itself in better. I used some canned air pointed in at the button to finish it off. My problem shoulder button now works great, with me being able to press the button from any angle and still register a click. Hope this helps someone.